STEMORIA scientific instrument

Integral Explorer

Connect accumulated signed area, analytic integration, and finite midpoint Riemann approximation.

Mathematics

Manipulate

Measure

Interpret

Linked scientific model

Integral Explorer

Connect definite integration to accumulated signed area and a finite midpoint Riemann approximation.

I2 · equation-driven modelone state · synchronized views

Primary scientific view

Function

live model output

Interactive measurement plotMove across the graph to inspect values

f(x) = quadratic

f(x) (dimensionless) vs x (dimensionless)

Probe the curve to read approximate model values at any x-position.

Integral

∫ₐᵇ f(x) dx

Midpoint sum: Σ f(xᵢ*) Δx. The exact value uses the analytic antiderivative for the intentionally limited function family.

Data

Exact integral

2.6667

Riemann sum

2.6563

Absolute error

0.010417

Interpretation

Predict before testing

For a smooth function, what generally happens to midpoint-sum error as the number of rectangles increases?

STEMORIA scientific instrument

Integral Explorer

Connect accumulated signed area, analytic integration, and finite midpoint Riemann approximation.

Mathematics

Manipulate

Measure

Interpret

Linked scientific model

Integral Explorer

Connect definite integration to accumulated signed area and a finite midpoint Riemann approximation.

I2 · equation-driven modelone state · synchronized views

Primary scientific view

Function

live model output

Interactive measurement plotMove across the graph to inspect values

f(x) = quadratic

f(x) (dimensionless) vs x (dimensionless)

Probe the curve to read approximate model values at any x-position.

Integral

∫ₐᵇ f(x) dx

Midpoint sum: Σ f(xᵢ*) Δx. The exact value uses the analytic antiderivative for the intentionally limited function family.

Data

Exact integral

2.6667

Riemann sum

2.6563

Absolute error

0.010417

Interpretation

Predict before testing

For a smooth function, what generally happens to midpoint-sum error as the number of rectangles increases?